A moment-matching method for model reduction of linear switched systems (LSSs) is presented. The method can be seen as a non-trivial extension of the Krylov subspace methods for linear time-invariant (LTI) systems. The procedure is based on the so called "nice selections," which represent a choice of basis in the reachability or observability space of the LSS. The framework can also be used for exact matching of the input-output behavior of an LSS with a reduced order LSS for a specific switching sequence. Conditions for applicability of the method for model reduction are stated and finally the results are illustrated on numerical examples.